Is this answer wrong?

[Vantage]

I was doing a binomial expansion worksheet, and I think one of these answers is wrong. I just want to make absolutely sure I'm not going crazy.
The above is wrong, is it not? [imath]\frac {8!}{3!5!}[/imath] does not equal [imath]\frac {56}{2}[/imath], it's just [imath]56[/imath]. Therefore the coefficient of [imath]k^3x^3[/imath] is [imath]56(64) = 3584[/imath], not [imath]28(64) = 1792[/imath] - if I'm not mistaken.

Thanks in advance for any help.

 

[Deleted member 4993]

I was doing a binomial expansion worksheet, and I think one of these answers is wrong. I just want to make absolutely sure I'm not going crazy.View attachment 28678
The above is wrong, is it not? [imath]\frac {8!}{3!5!}[/imath] does not equal [imath]\frac {56}{2}[/imath], it's just [imath]56[/imath]. Therefore the coefficient of [imath]k^3x^3[/imath] is [imath]56(64) = 3584[/imath], not [imath]28(64) = 1792[/imath] - if I'm not mistaken.

Thanks in advance for any help.

\(\displaystyle \frac{8!}{3!5!} \ = \ \frac{8 * 7 * 6 *(5!)}{3!5!} \ = \frac{8 * 7 * 6}{3 * 2 * 1} \)

You are correct

 

[Vantage]

\(\displaystyle \frac{8!}{3!5!} \ = \ \frac{8 * 7 * 6 *(5!)}{3!5!} \ = \frac{8 * 7 * 6}{3 * 2 * 1} \)

You are correct

Thank you. I was worried I was missing something obvious.